Trains Boats and Streams Practice Test 4 with solutions

Let the speed of the train be S km/hr and the distance travelled is D km.
Total time taken = $\frac{\mathit{D}}{\mathit{S}}$ hrs
First Case:
$\frac{150}{\mathit{S}}+\left(\frac{\mathit{D}-150}{3\mathit{S}}\right)\times 5$ = $\frac{\mathit{D}}{\mathit{S}}+8$
450 + 5D - 750 = 3D + 24S
2D - 24S = 750 - 450 = 300
2D - 24S = 300 ......(i)
Second Case:
$\frac{510}{\mathit{S}}+\left(\frac{\mathit{D}-510}{3\mathit{S}}\right)\times 5$ = $\frac{\mathit{D}}{\mathit{S}}+4$
1,530 + 5D - 2,550 = 3D + 12S
2D - 12S = 2,550 -1,530 = 1,020 ……(ii)
From (i) and (ii) we get,
12S = 720
S = 60 km/hr.
⇒ 2D = 300 + 24S
= 300 + 24 × 60
2D = 1,740
D = 870 km